∠CAE = 120°
∠CAD = 60°
∠BAE = 180°
∠DEC = 30°
We start out with the fact that points C and D split the semicircle into 3 sections. This means that ∠BAC, ∠CAD and ∠DAE are all 60° (180/3 = 60).
Since it forms a straight line, ∠BAE is 180°.
Since it is formed by ∠CAD and ∠DAE, ∠CAE = 60+60 = 120°.
We know that an inscribed angle is 1/2 of the corresponding arc; since CD is 1/3 of the circle, it is 1/3(180) = 60; and this means that ∠DEC = 30°.
To answer this question you should know what to do to change the polar coordinates to rectangular ones: x = rcos (θ)
y = rsen (θ)
So for r = -2 and θ = 2π we have
x = -2cos (2π)
x = -2
y = -2sen (2π)
y = 0
Finally the equivalent point in Cartesian coordinates is the point:
(-2 0)
The correct answer is option B
The radius of a circle is half the length of the circumference.
So multiply 12 by itself and you get 24.
The answer is C.
They are dependent events, because the probability of the second event depends on the result of the first event
If you replace the marble before picking up the second marble, then the first event didn't affect the second result ant the events were independent.
Given that you did not replace the marble, the second pick up has different probailities depending on the first result.